b-Symbol Distance of Constacylic Codes of Length p<sup>s</sup> Over F<sub>p</sub><sup>m</sup> &#x002B; uF<sub>p</sub><sup>m</sup>

In this research paper, the repeated-root constacyclic codes over the chain ring F<sub>p</sub>m + uF<sub>p</sub>m are considered, where p is a prime and m &gt; 0 is any integer. The b-symbol distance for prime power length, i.e. p<sup>s</sup> is also studied f...

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Bibliographic Details
Main Authors: H. Q. Dinh, Atul Gaur, A. K. Singh, Manoj Kumar Singh, W. Yamaka
Format: Article
Language:English
Published: IEEE 2020-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/9057447/
Description
Summary:In this research paper, the repeated-root constacyclic codes over the chain ring F<sub>p</sub>m + uF<sub>p</sub>m are considered, where p is a prime and m &gt; 0 is any integer. The b-symbol distance for prime power length, i.e. p<sup>s</sup> is also studied for any integer s &gt; 0. The Hamming and symbol-pair distances of all &#x03B4;-constacyclic codes have been thoroughly studied in [18], where &#x03B4; is an unit in the ring F<sub>p</sub>m + uF<sub>p</sub>m which is of the form &#x03B6; and &#x03C6; + u&#x03C6;, where 0 &#x2260; 6 &#x03C6;, &#x03C6;, &#x03B6; &#x2208; F<sub>p</sub>m. In this paper, the b-symbol distance of all such &#x03B4;-constacyclic codes of prime power length is computed for 1 &#x2264; b &#x2264; &#x230A;p/2&#x230B;. Furthermore, as an application, all MDS b-symbol constacyclic codes of length p<sup>s</sup> over F<sub>p</sub>m + uF<sub>p</sub>m are established.
ISSN:2169-3536